On the Mathematical Modeling of Measles Disease Dynamics with Encephalitis and Relapse Under the Atangana–Baleanu–Caputo Fractional Operator and Real Measles Data of Nigeria

Ogunmiloro, Oluwatayo Michael; Idowu, A. S.; Ogunlade, Temitope Olu; Akindutire, Roselyn Opeyemi

doi:10.1007/s40819-021-01122-2

Cited by 17 publications

(4 citation statements)

References 26 publications

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“…Farman et al [17] developed and provided a numerical solution of an SEIR epidemic model with non-integer temporal fractional derivatives to control measles in infected populations. Ogunmiloro et al [18] investigated two groups of measles-infected and measles-induced encephalitis-infected people with recurrence under the Atangana-Baleanu-Caputo (ABC) fractional operator, explaining measles propagation dynamics with a double dose of vaccination. Using the Caputo fractional derivative, Qureshi built an epidemiological model for a measles epidemic [19].…”

Section: Introductionmentioning

confidence: 99%

Modelling and Analysis of a Measles Epidemic Model with the Constant Proportional Caputo Operator

et al. 2023

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Despite the existence of a secure and reliable immunization, measles, also known as rubeola, continues to be a leading cause of fatalities globally, especially in underdeveloped nations. For investigation and observation of the dynamical transmission of the disease with the influence of vaccination, we proposed a novel fractional order measles model with a constant proportional (CP) Caputo operator. We analysed the proposed model’s positivity, boundedness, well-posedness, and biological viability. Reproductive and strength numbers were also verified to examine how the illness dynamically behaves in society. For local and global stability analysis, we introduced the Lyapunov function with first and second derivatives. In order to evaluate the fractional integral operator, we used different techniques to invert the PC and CPC operators. We also used our suggested model’s fractional differential equations to derive the eigenfunctions of the CPC operator. There is a detailed discussion of additional analysis on the CPC and Hilfer generalised proportional operators. Employing the Laplace with the Adomian decomposition technique, we simulated a system of fractional differential equations numerically. Finally, numerical results and simulations were derived with the proposed measles model. The intricate and vital study of systems with symmetry is one of the many applications of contemporary fractional mathematical control. A strong tool that makes it possible to create numerical answers to a given fractional differential equation methodically is symmetry analysis. It is discovered that the proposed fractional order model provides a more realistic way of understanding the dynamics of a measles epidemic.

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Section: Introductionmentioning

confidence: 99%

Modelling and Analysis of a Measles Epidemic Model with the Constant Proportional Caputo Operator

et al. 2023

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“…Few researchers have proposed a deterministic models by considering the transmission dynamics of the disease with double dose vaccination [5,7]. Other related studies on the dynamics of measles can be found in [26][27][28][29]. The current study aims to examine the impact of certain prevention measures, including vaccination and contact rate, for effective measles control.…”

Section: Introductionmentioning

confidence: 99%

Analysis and dynamics of measles with control strategies: a mathematical modeling approach

Peter

Panigoro

Ibrahim

et al. 2023

Int. J. Dynam. Control

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In this work, we examine the impact of certain preventive measures for effective measles control. To do this, a mathematical model for the dynamics of measles transmission is developed and analyzed. A suitable Lyapunov function is used to establish the global stability of the equilibrium points. Our analysis shows that the disease-free equilibrium is globally stable, with the measles dying out on the long run because the reproduction number R 0 ≤ 1. The condition for the global stability of the endemic equilibrium is also derived and analyzed. Our findings show that when R 0 > 1, the endemic equilibrium is globally stable in the required feasible region. In this situation, measles will spread across the populace. A numerical simulation was performed to demonstrate and support the theoretical findings. The results suggest that lowering the effective contact with an infected person and increasing the rate of vaccinating susceptible people with high-efficacy vaccines will lower the prevalence of measles in the population.

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“…The ABC-fractional derivative produces better results in many real-world problems. [12][13][14][15][16][17][18][19][20][21][22][23] Jose et al 8 developed and tested a mathematical model for SA transmission dynamics in humans in 2021. The goal of the study is to look into the effects of awareness and strong determination, two cognitive traits that have a greater impact on preventing substance abuse.…”

Section: Introductionmentioning

confidence: 99%

“…Atangana and Baleanu 11 were the first to employ a fractional‐order derivative in the context of a non‐singular and non‐local kernel, using the rule of an extended Mittag‐Leffler function. The ABC‐fractional derivative produces better results in many real‐world problems 12–23 …”

Section: Introductionmentioning

confidence: 99%

Computational dynamics of a fractional order substance addictions transfer model with Atangana‐Baleanu‐Caputo derivative

Jose

Raja

Băleanu

et al. 2022

Math Methods in App Sciences

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In this paper, the ABC fractional derivative is used to provide a mathematical model for the dynamic systems of substance addiction. The basic reproduction number is investigated, as well as the equilibrium points' stability. Using fixed point theory and nonlinear analytic techniques, we verify the theoretical results of solution existence and uniqueness for the proposed model. A numerical technique for getting the approximate solution of the suggested model is established by using the Adams type predictor‐corrector rule for the ABC‐fractional integral operator. There are several numerical graphs that correspond to different fractional orders. Furthermore, we present a numerical simulation for the transmission of substance addiction in two scenarios with fundamental reproduction numbers greater than and fewer than one.

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On the Mathematical Modeling of Measles Disease Dynamics with Encephalitis and Relapse Under the Atangana–Baleanu–Caputo Fractional Operator and Real Measles Data of Nigeria

Cited by 17 publications

References 26 publications

Modelling and Analysis of a Measles Epidemic Model with the Constant Proportional Caputo Operator

Modelling and Analysis of a Measles Epidemic Model with the Constant Proportional Caputo Operator

Analysis and dynamics of measles with control strategies: a mathematical modeling approach

Computational dynamics of a fractional order substance addictions transfer model with Atangana‐Baleanu‐Caputo derivative

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